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if x is an integer, which value of x will yield the largest

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if x is an integer, which value of x will yield the largest [#permalink] New post   31 Jul 2008, 10:42
if x is an integer, which value of x will yield the largest value for 5^-(x-3)^2

x= 3, -3, 9, -9, 0

Note: I saw something similar to this on my own exam..the numbers are made-up of course, the function is madeup also..just trying to test the concept..



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Re: if x is an integer, which value of x will yield the largest [#permalink] New post   31 Jul 2008, 10:50
I think the answer would be 3.

regardless of x being greater or less than 3, the - in the front will switch the sign after squaring and make the exponent negative for sure. So we will have \(\frac{1}{5^n}\) where \(n = (x-3)^2\)

If x = 3, then we have -(3-3)^2, or 0^2 = 0, and -0 = 0, and so we then have \(\frac{1}{5^0} = 1/1 = 1\).

Every other value listed for x will give an actual power making 5 * 5 * 5 * 5 or whatever that value becomes. With 5 being in the denominator, the largest fraction will be the one with the smallest denominator.

fresinha12 wrote:
if x is an integer, which value of x will yield the largest value for 5^-(x-3)^2

x= 3, -3, 9, -9, 0

Note: I saw something similar to this on my own exam..the numbers are made-up of course, the function is madeup also..just trying to test the concept..
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Re: if x is an integer, which value of x will yield the largest [#permalink] New post   31 Jul 2008, 10:51
fresinha12 wrote:
if x is an integer, which value of x will yield the largest value for 5^-(x-3)^2

x= 3, -3, 9, -9, 0

Note: I saw something similar to this on my own exam..the numbers are made-up of course, the function is madeup also..just trying to test the concept..


If I'm reading this right 5^-(x-3)^2 = 1/(5^(x-3)^2)
That means you're trying to minimize 5^(x-3)^2
And from that, you're trying to minimize |x-3|

Of the answer choices, 3 would be the best choice.
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Re: if x is an integer, which value of x will yield the largest [#permalink] New post   31 Jul 2008, 10:52
I think answer is 3.

5^-(x-3)^2 => 1/5^(x-3)^2

1/5^(x-3)^2 => 3 makes the denominator 1 other values greater than 1.
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Re: if x is an integer, which value of x will yield the largest [#permalink] New post   31 Jul 2008, 11:01
fresinha12 wrote:
if x is an integer, which value of x will yield the largest value for 5^-(x-3)^2

x= 3, -3, 9, -9, 0

Note: I saw something similar to this on my own exam..the numbers are made-up of course, the function is madeup also..just trying to test the concept..


to get the largest value of the function f(x)=5^-(x-3)^2

(x-3)^2 should be minimum.hence x=3 is the correct value
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Re: if x is an integer, which value of x will yield the largest [#permalink] New post   31 Jul 2008, 11:01
mbathlagamt08 - Welcome to GMAT club!

mbathlagmat08 wrote:
I think answer is 3.

5^-(x-3)^2 => 1/5^(x-3)^2

1/5^(x-3)^2 => 3 makes the denominator 1 other values greater than 1.
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Re: if x is an integer, which value of x will yield the largest [#permalink] New post   31 Jul 2008, 11:28
fresinha12 wrote:
if x is an integer, which value of x will yield the largest value for 5^-(x-3)^2

x= 3, -3, 9, -9, 0

Note: I saw something similar to this on my own exam..the numbers are made-up of course, the function is madeup also..just trying to test the concept..


1) Largest value 5^-(x-3)^2 = when (x-3)^2 is least value..

(x-3) ^2 least value =0 --> when x=3.
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Re: if x is an integer, which value of x will yield the largest [#permalink] New post   31 Jul 2008, 12:02
i agree with my example ans should be 3...

however on the exam..the ans choice listed didnt make (x-N)^2=0..i spent about 2 mins and just guessed..i think i was dubed by gmac..my exam was buggy..
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Re: if x is an integer, which value of x will yield the largest [#permalink] New post   31 Jul 2008, 12:07
fresinha12 wrote:
i agree with my example ans should be 3...

however on the exam..the ans choice listed didnt make (x-N)^2=0..i spent about 2 mins and just guessed..i think i was dubed by gmac..my exam was buggy..



(x-N)^2=0 are you sure that power is 2 or -2 power.

(x-n)^-2 in this case.. answer could be different.



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